YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(6) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(a(b(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(a(b(a(b(a(b(x1)))))))))))))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))

Q is empty.

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(5) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
147, 148, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239

Node 147 is start node and node 148 is final node.

Those nodes are connected through the following edges:

* 147 to 207 labelled b_1(0)* 148 to 148 labelled #_1(0)* 207 to 208 labelled a_1(0)* 208 to 209 labelled b_1(0)* 209 to 210 labelled a_1(0)* 210 to 211 labelled b_1(0)* 211 to 212 labelled a_1(0)* 212 to 213 labelled b_1(0)* 213 to 214 labelled a_1(0)* 213 to 229 labelled b_1(1)* 214 to 215 labelled a_1(0)* 214 to 229 labelled b_1(1)* 215 to 216 labelled a_1(0)* 215 to 229 labelled b_1(1)* 216 to 217 labelled a_1(0)* 216 to 229 labelled b_1(1)* 217 to 148 labelled a_1(0)* 217 to 229 labelled b_1(1)* 229 to 230 labelled a_1(1)* 230 to 231 labelled b_1(1)* 231 to 232 labelled a_1(1)* 232 to 233 labelled b_1(1)* 233 to 234 labelled a_1(1)* 234 to 235 labelled b_1(1)* 235 to 236 labelled a_1(1)* 235 to 229 labelled b_1(1)* 236 to 237 labelled a_1(1)* 236 to 229 labelled b_1(1)* 237 to 238 labelled a_1(1)* 237 to 229 labelled b_1(1)* 238 to 239 labelled a_1(1)* 238 to 229 labelled b_1(1)* 239 to 148 labelled a_1(1)* 239 to 229 labelled b_1(1)


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(6)
YES